Welcome to our Physics lesson on Magnetic Field Inside a Long Straight Wire with Current, this is the fourth lesson of our suite of physics lessons covering the topic of Ampere's Law, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
In this case, the radius r of Amperian loop is smaller than the radius R of wire. This means the Amperian loop is taken inside the wire's section.
Like in the previous paragraph, the distribution of magnetic field has a cylindrical symmetry as the current is uniformly distributed throughout the wire (the direction is out of page). Therefore, we use a similar approach as in the calculation of magnetic field outside the wire discussed in the previous paragraph.
Using Ampere's law for this situation, we obtain for r < R:
Since the current distribution is uniform, the current enclosed in the loop is proportional to the area of loop at any point, i.e.
or
Substituting this value for current in the previous formula obtained after integrating Ampere's law equation, yields
or
The above formula means the magnetic field is zero at centre of cross section of the wire and it has a maximum value for r = R (on the outer surface of wire). This is another proof that the electric charges (that are responsible for the magnetic field generation) are concentrated on the outer layer of conductor, as we have explained in Section 14.
You have reached the end of Physics lesson 16.6.4 Magnetic Field Inside a Long Straight Wire with Current. There are 5 lessons in this physics tutorial covering Ampere's Law, you can access all the lessons from this tutorial below.
Enjoy the "Magnetic Field Inside a Long Straight Wire with Current" physics lesson? People who liked the "Ampere's Law lesson found the following resources useful:
We hope you found this Physics lesson "Ampere's Law" useful. If you did it would be great if you could spare the time to rate this physics lesson (simply click on the number of stars that match your assessment of this physics learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of physics and other disciplines.